The HalfCheetahRandV el environment was introduced in Finn et al. The Walker2DRandParams environment is defined similarly. For full descriptions of the ProMP and TRPO-MAML algorithms, please refer to the cited papers. We use the implementations in the codebase provided by Rothfuss et al. Each iteration of ProMP (TRPO-MAML) requires twice as many steps from the simulator as DRS+PPO (DRS+TRPO).

D. Belomestny, L. Iosipoi † E. Moulines ‡, A. Naumov §, and S. Samsonov ¶ Abstract In this paper we propose a novel variance reduction approach for additive functionals of Markov chains based on minimization of an estimate for the asymptotic variance of these functionals over suitable classes of control variates. A distinctive feature of the proposed approach is its ability to significantly reduce the overall finite sample variance. This feature is theoretically demonstrated by means of a deep non asymptotic analysis of a variance reduced functional as well as by a thorough simulation study. In particular we apply our method to various MCMC Bayesian estimation problems where it favourably compares to the existing variance reduction approaches. 1 Introduction Variance reduction methods play nowadays a prominent role as a complexity reduction tool in simulation based numerical algorithms like Monte Carlo (MC) or Markov Chain Monte Carlo (MCMC).

The notion of DPP was first introduced by [Mac75] to model fermions. Since then, They have been extensively studied, and efficient algorithms have been discovered for tasks like sampling from DPPs [LJS15, DR10, AGR16], marginalization [BR05], and learning [GKFT14, UBMR17] them (in the discrete domain). In machine learning they are mainly used to solve problems where selecting a diverse set of objects is preferred since they offer negative correlation. To get intuition about why they are good models to capture diversity, suppose each row of the gram matrix associated with the kernel is a feature vector representing an item. It means the probability of a set of items is proportional to the square of the volume of the space spanned the vectors representing items. Therefore, larger volume shows those items are more spread which resembles diversity.

The problem of Non-Gaussian Component Analysis (NGCA) is about finding a maximal low-dimensional subspace $E$ in $\mathbb{R}^n$ so that data points projected onto $E$ follow a non-gaussian distribution. Although this is an appropriate model for some real world data analysis problems, there has been little progress on this problem over the last decade. In this paper, we attempt to address this state of affairs in two ways. First, we give a new characterization of standard gaussian distributions in high-dimensions, which lead to effective tests for non-gaussianness. Second, we propose a simple algorithm, \emph{Reweighted PCA}, as a method for solving the NGCA problem. We prove that for a general unknown non-gaussian distribution, this algorithm recovers at least one direction in $E$, with sample and time complexity depending polynomially on the dimension of the ambient space. We conjecture that the algorithm actually recovers the entire $E$.